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It's not entirely clear where your trip ends, but if you're flying out directly from Kyushu, you are probably better off purchasing the JR Kyushu Rail Pass instead. If you do need to return to Osaka, you should probably get the JR Rail Pass.
The "northern Kyushu pass" is ¥7,200/9,260 for 3/5 days and covers Beppu, Aso and Kumamoto. If you want to go to Sakurajima (Kagoshima), you'll need to get the full Kyushu pass, which is twice as expensive at ¥14,400/17,490.
To get to Kyushu, a one-way fare from Shin-Osaka to Hakata (Fukuoka) on the fastest Nozomi service (unreserved seat) is ¥14,480, with a few extra yen if you split the journey at Hiroshima, or a few yen less if you only buy your ticket to Shimonoseki and start using a Kyushu pass there. So this plus a 5-day northern Kyushu pass would only cost you ¥23,740.
If you do have to backtrack to Osaka, the return alone will cost you ¥28,960, meaning paying ¥29,110 for a 7-day JR pass that gets you access to all of Kyushu is a no-brainer.